A fredholm alternative-like result on power bounded operators

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Abstract

Let X be a complex Banach space and T : X -> X be a power bounded operator, i.e., sup(n >= 0) parallel to T(m)parallel to < infinity. We write B(X) for the Banach algebra of all bounded linear operators on X. We prove that the space Ran(I - T) is closed if and only if there exist a projection theta is an element of B(X) and an invertible operator R is an element of B(X) such that I - T = theta R = R theta. This paper also contains some consequences of this result.

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• A fredholm alternative-like result on power bounded operators. (deposited 21 Jul 2010 10:01)
  • A fredholm alternative-like result on power bounded operators. (deposited 18 Nov 2011 22:06) [Currently Displayed]